Identify Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It has the form: (a + b)² = a² + 2ab + b².

$$x^2 + 16x + 64$$ is a perfect square trinomial because it can be factored as (x + 8)².

$$x^2 + 26x + 169$$ is a perfect square trinomial because it can be factored as (x + 13)².

$$x^2 + 12x + 36$$ is a perfect square trinomial because it can be factored as (x + 6)².

$$x^2 + 16x + 64$$ is a perfect square trinomial because it can be factored as (x + 8)².

$$x^2 + 6x + 9$$ is a perfect square trinomial because it can be factored as (x + 3)².

The general form of a perfect square trinomial is: a² + 2ab + b², which factors to (a + b)².

To identify a perfect square trinomial, check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.

The roots of $$x^2 + 16x + 64$$ are x = -8 (a double root) because it can be factored as (x + 8)².

In a perfect square trinomial of the form $$x^2 + 2ax + a^2$$ , the coefficient of x is 2a and the constant term is a².